ECE532 Biomedical Optics © 1998 Steven L. Jacques, Scott A. Prahl Oregon Graduate Institute

The math of Mie scattering

Consider a source, a spherical scattering particle, and an observer whose three positions define a plane called the scattering plane. Incident light and scattered light can be reduced to their components which are parallel or perpendicular to the scattering plane. As shown in the following figure, the parallel and perpendicular components can be experimentally selected by a linear polarization filter oriented parallel or perpendicular to the scattering plane.

The Scattering matrix describes the relationship between incident and scattered electric field components perpendicular and parallel to the scattering plane as observed in the "far-field" (ref: Bohren and Huffman):

The above expression simplifies in practical experiments:

• The exponential term, -exp(-ik(r-z))/ikr, is a transport factor that depends on the distance between scatterer and observer. If one measures scattered light at a contant distance r from the scatterer, eg., as a function of angle or orientation of polarization, then the transport factor becomes a constant.
  
  
• The total field (E_tot) depends on the incident field (E_i), the scattered field (E_s) , and the interaction of these fields (E_int). If one observes the scattering from a position which avoids E_i, then both E_i and E_int are zero and only E_s is observed.
  
  
• For "far-field" observation of E_s at a distance r from a particle of diameter d such that kr >> n_c², k = 2π/, n_c = d/, the scattering elements S₃ and S₄ equal zero (see Eq. 4.75, Bohren and Huffman).
  
  
• Practical experiments measure intensity, I = <E E*> = (1/2)a², where E = a exp(-i), and a is amplitude and is phase of the electric field.

Hence for practical scattering measurements, the above equation simplifies to the following:

Mie theory yields two sets of descriptors of scattering:

ANGULAR SCATTERING PATTERN OF POLARIZED LIGHT

EFFICIENCIES OF SCATTERING AND ABSORPTION